Modeling Photonic Quantum Information Processing Experiments Using Gaussian Characteristic Functions

Single optical photons are currently the best possible candidates for long distance quantum information exchange due to low interactions with each other and with the environment. In practice, single photon states are difficult to create, meaning that often in experiments more accessible states are used to approximate single photon states, such as weak coherent states or two mode squeezed vacuum states. Since these states are Gaussian and all underlying operations, including experimental imperfections and measurements, can be described as Gaussian processes, phase space methods can be used to model photonic quantum information processes. In particular, we use the characteristic function approach to model the effects of using photon number resolving detectors (PNR’s) to improve the purity of heralded single photon sources based on spontaneous parametric down conversion (SPDC). We further use this approach to examine the possible improvements of using PNR’s in the Hong-Ou-Mandel interference experiment that can be used to estimate photon indistinguishability. In addition to PNR related models, we also extend the previous teleportation model to include entanglement swapping protocols so we can estimate the fidelity of the process.